There are two basic parkerizing processes, zinc phosphate and manganese phosphate. Zinc phosphating (rarely used now)will yield a larger grain, grey hue where the manganese phosphate will yield a finer grained dark charcoal to black color. The greenish hue seen on older firearms is typically zinc phosphate that has been exposed to cosmoline/oils for long periods.
You can get dyes that are a pre or post treatment to the parkerizing that will lend a greenish tint to manganese phosphating. There are also a variety of homespun witches brews folks use to get the tint.